From a Republican perspective though, Pawlenty remains well-liked on the GOP side and is probably remembered more fondly than Coleman, partly because Pawlenty was just a more interesting political figure.
However one argument that Pawlenty is past his prime can be found in the differences between his map and Trump's map. It's possible that in the post-Obama era, the urban and suburban voters around Minneapolis/St. Paul who voted for Pawlenty won't be coming back to the Republicans, even for one of their own.
Here's Pawlenty's 2006 victory map:
And here's Trump's 2016 map:
These appear to be very different coalitions. Trump traded pretty much the entire Twin Cities area for the rural voters up north. Bad deal in Minnesota for Trump but a good deal in other states. In any case, can Pawlenty win back his Twin Cities voters, or does he have to try to win with Trumpy voters, similar to Ed Gillespie?